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2024/homework.html

@@ -213,8 +213,8 @@ <h1 class="title">Homework Overview</h1>
 
 
 <p>Here is an overview of all Homework up to date:</p>
-<p><strong>Hw 1</strong>: <a href="../2024/homework/homework01.html">here</a></p>
-<p>TBD</p>
+<p><strong>Hw 1: Google Colab</strong>: <a href="../2024/homework/homework01.html">here</a></p>
+<p><strong>Hw 2: Neural Networks</strong>: <a href="../2024/homework/homework02.html">here</a></p>
 
 
 

2024/weeks/week02/slides.html

@@ -359,131 +359,163 @@ <h1 class="title"><font style="font-size:1em;">Week 02<br> Basics of Neural Netw
 <nav role="doc-toc"> 
 <h2 id="toc-title">What we will cover today:</h2>
 <ul>
-<li><a href="#/mathematical-concepts" id="/toc-mathematical-concepts">Mathematical concepts</a></li>
+<li><a href="#/machine-learning" id="/toc-machine-learning">Machine learning</a></li>
 <li><a href="#/neural-networks" id="/toc-neural-networks">Neural Networks</a></li>
 </ul>
 </nav>
 </section>
-<section>
-<section id="mathematical-concepts" class="title-slide slide level1 smaller">
-<h1>Mathematical concepts</h1>
+<section class="slide level2">
 
-</section>
-<section id="section" class="slide level2 smaller">
-<h2></h2>
-<p><strong>Scalars</strong>: single number</p>
-<p><span class="math display">\[
+<!-- 
+# Mathematical concepts {.smaller}
+
+## {.smaller}
+
+**Scalars**: single number
+
+$$
 x = 1
-\]</span></p>
-<p><strong>Vectors</strong>: sequence of numbers</p>
-<p><span class="math display">\[
+$$
+
+**Vectors**: sequence of numbers
+
+$$
 v = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}
-\]</span></p>
-<p><strong>Matrix</strong>: 2D array of numbers</p>
-<p><span class="math display">\[
-M = \begin{bmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \end{bmatrix}
-\]</span></p>
-</section>
-<section id="section-1" class="slide level2 smaller">
-<h2></h2>
-<p><strong>Matrix multiplication</strong></p>
-<p><span class="math display">\[
-\begin{bmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \end{bmatrix} \times \begin{bmatrix} 1 &amp; 2 \\ 3 &amp; 4 \\ 5 &amp; 6 \end{bmatrix}
-\]</span></p>
-<p><span class="math display">\[
-= \begin{bmatrix} 22 &amp; 28 \\ 49 &amp; 64 \end{bmatrix}
-\]</span></p>
-<ul>
-<li>The first matrix has 2 rows and 3 columns, and the second matrix has 3 rows and 2 columns.</li>
-<li>The number of columns in the first matrix should be equal to the number of rows in the second matrix.</li>
-<li>The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.</li>
-</ul>
+$$
+
+**Matrix**: 2D array of numbers
+
+$$
+M = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}
+$$
+
+## {.smaller}
+
+**Matrix multiplication**
+
+
+$$
+\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \times \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}
+$$
+
+$$
+= \begin{bmatrix} 22 & 28 \\ 49 & 64 \end{bmatrix}
+$$
+
+- The first matrix has 2 rows and 3 columns, and the second matrix has 3 rows and 2 columns.
+- The number of columns in the first matrix should be equal to the number of rows in the second matrix.
+- The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
+
+## {.smaller}
+
+**Element-wise multiplication**
+
+$$
+\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \odot \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}
+$$
+
+$$
+= \begin{bmatrix} 1 & 4 & 9 \\ 16 & 25 & 36 \end{bmatrix}
+$$
+
+- The matrices should have the same dimensions.
+- The resulting matrix will have the same dimensions as the input matrices.
+- You multiply the corresponding elements of the matrices.
+
+## {.smaller}
+
+**Matrix addition**
+
+$$
+\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} + \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}
+$$
+
+$$
+= \begin{bmatrix} 2 & 4 & 6 \\ 8 & 10 & 12 \end{bmatrix}
+$$
+
+- You add the corresponding elements of the matrices.
+
+## {.smaller}
+
+**Dot product**
+
+$$
+\begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}
+$$
+
+$$
+= 1 \times 1 + 2 \times 2 + 3 \times 3 = 14
+$$
+
+- The number of columns in the first matrix should be equal to the number of rows in the second matrix.
+- The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
+- You multiply the corresponding elements of the matrices and sum them up. -->
 </section>
-<section id="section-2" class="slide level2 smaller">
-<h2></h2>
-<p><strong>Element-wise multiplication</strong></p>
-<p><span class="math display">\[
-\begin{bmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \end{bmatrix} \odot \begin{bmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \end{bmatrix}
-\]</span></p>
-<p><span class="math display">\[
-= \begin{bmatrix} 1 &amp; 4 &amp; 9 \\ 16 &amp; 25 &amp; 36 \end{bmatrix}
-\]</span></p>
+<section id="machine-learning" class="title-slide slide level1">
+<h1>Machine learning</h1>
 <ul>
-<li>The matrices should have the same dimensions.</li>
-<li>The resulting matrix will have the same dimensions as the input matrices.</li>
-<li>You multiply the corresponding elements of the matrices.</li>
-</ul>
-</section>
-<section id="section-3" class="slide level2 smaller">
-<h2></h2>
-<p><strong>Matrix addition</strong></p>
-<p><span class="math display">\[
-\begin{bmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \end{bmatrix} + \begin{bmatrix} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \end{bmatrix}
-\]</span></p>
-<p><span class="math display">\[
-= \begin{bmatrix} 2 &amp; 4 &amp; 6 \\ 8 &amp; 10 &amp; 12 \end{bmatrix}
-\]</span></p>
+<li>Using <strong>learning algorithms</strong> to learn from existing data and predict for new data.</li>
+<li>We have seen two types of Machine Learning models:
 <ul>
-<li>You add the corresponding elements of the matrices.</li>
+<li><strong>Statistical language models</strong></li>
+<li><strong>Probabilistic language models</strong></li>
+</ul></li>
+<li>Today: Neural Networks</li>
 </ul>
+<!-- ->who remembers what a statistical/probabilistic language model is? What is their "learning algorithm"?-->
 </section>
-<section id="section-4" class="slide level2 smaller">
-<h2></h2>
-<p><strong>Dot product</strong></p>
-<p><span class="math display">\[
-\begin{bmatrix} 1 &amp; 2 &amp; 3 \end{bmatrix} \cdot \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}
-\]</span></p>
-<p><span class="math display">\[
-= 1 \times 1 + 2 \times 2 + 3 \times 3 = 14
-\]</span></p>
-<ul>
-<li>The number of columns in the first matrix should be equal to the number of rows in the second matrix.</li>
-<li>The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.</li>
-<li>You multiply the corresponding elements of the matrices and sum them up.</li>
-</ul>
-</section></section>
+
 <section>
-<section id="neural-networks" class="title-slide slide level1">
+<section id="neural-networks" class="title-slide slide level1 smaller">
 <h1>Neural Networks</h1>
-<ul>
-<li>Neural networks are a class of machine learning models inspired by the human brain.</li>
-</ul>
-<p><strong>How do neural networks work?</strong></p>
-<ul>
-<li><strong>Input</strong>: The network receives data (like an image or text).</li>
-<li><strong>Processing</strong>: The data is processed through a series of layers.</li>
-<li><strong>Output</strong>: The network produces an output (like a prediction or classification).</li>
-</ul>
-</section>
-<section id="section-5" class="slide level2 smaller">
-<h2></h2>
-<p><strong>Learning</strong></p>
+<p>Neural networks are a class of machine learning models inspired by the human brain.</p>
+<p><br></p>
+<p><strong>Learning Alorithm</strong></p>
 <ul>
 <li>Neural networks learn by looking at many examples.</li>
-<li>They adjust their internal settings to improve their accuracy.</li>
-<li>This process is called training.</li>
-</ul>
-<p><strong>Components of a neural network</strong></p>
-<ul>
-<li><strong>Neurons</strong>: Basic building blocks of a neural network.</li>
-<li><strong>Layers</strong>: Neurons are organized into layers.</li>
-<li><strong>Weights and biases</strong>: Parameters that the network learns during training.</li>
+<li>They adjust their internal settings (= <strong>parameters</strong>) to improve their accuracy.</li>
+<li>This is process is called <strong>training</strong>.</li>
 </ul>
 <p><strong>Advantages of neural networks</strong></p>
 <ul>
 <li>Can learn complex patterns.</li>
 <li>Can generalize to new data.</li>
-<li>Can be used for a wide range of tasks (like image recognition, speech recognition, and natural language processing).</li>
+<li>Can be used for a wide range of tasks (speech recognition, and natural language processing).</li>
 </ul>
 </section>
-<section id="section-6" class="slide level2 smaller">
+<section id="architecture" class="slide level2">
+<h2>Architecture</h2>
+<p><br> <img src="nn.png"> <br> The input can be a vector, and the output some classification, like a corresponding animal.</p>
+</section>
+<section id="section" class="slide level2">
 <h2></h2>
-<p><strong>Perceptron</strong></p>
-<div class="cell" data-reveal="true" data-layout-align="center">
-<div class="cell-output-display">
-<div>
-<p></p><figure class=""><p></p>
-<div>
+<p><br> <img src="nn_layers.png"> Every Neural Network has <strong>Layers</strong>. They are responsible for a specific action, like addition, and pass information to eachother. <br></p>
+</section>
+<section id="section-1" class="slide level2">
+<h2></h2>
+<p><br> <img src="nn_neurons.png"> Layers consist of <strong>neurons</strong> which each modify the input in some way. <br></p>
+</section>
+<section id="section-2" class="slide level2">
+<h2></h2>
+<p><br> <img src="nn_perceptron.png"> The simplest Neural network only has one layer with one neuron. This single neuron is called a <strong>perceptron</strong>. <br></p>
+</section>
+<section id="perceptron" class="slide level2">
+<h2>Perceptron</h2>
+<!-- 
+
+
+
+
+::::::{.cell reveal=true layout-align="center"}
+
+:::::{.cell-output-display}
+
+::::{}
+`<figure class=''>`{=html}
+
+:::{}
+
 <pre class="mermaid mermaid-js">graph LR
     subgraph Inputs
         x1((x1))
@@ -511,19 +543,25 @@ <h2></h2>
     style act fill:#98FB98,stroke:#333,stroke-width:2px
     style b fill:#FFFF00,stroke:#333,stroke-width:2px
 </pre>
-</div>
-<p></p></figure><p></p>
-</div>
-</div>
-</div>
-<ul>
-<li>Input Nodes (x1, x2, x3): Each input is a number.</li>
-<li>Weights (w1, w2, w3): Each weight is a number that determines the importance of the corresponding input.</li>
-<li>Bias (b): A constant value that shifts the output of the perceptron.</li>
-<li>Sum Node (Σ): Calculates the weighted sum of the inputs and the bias.</li>
-<li>Activation Function: Introduces non-linearity to the output of the perceptron.</li>
-<li>Output Node: The final output of the perceptron.</li>
-</ul>
+:::
+`</figure>`{=html}
+::::
+:::::
+::::::
+
+
+
+
+
+
+
+- Input Nodes (x1, x2, x3): Each input is a number.
+- Weights (w1, w2, w3): Each weight is a number that determines the importance of the corresponding input.
+- Bias (b): A constant value that shifts the output of the perceptron.
+- Sum Node (Σ): Calculates the weighted sum of the inputs and the bias.
+- Activation Function: Introduces non-linearity to the output of the perceptron.
+- Output Node: The final output of the perceptron.
+-->
 </section>
 <section id="activation-functions" class="slide level2 smaller">
 <h2>Activation functions</h2>
@@ -544,7 +582,7 @@ <h2>Activation functions</h2>
 <li>It is used in the output layer of a binary classification problem.</li>
 </ul>
 </section>
-<section id="section-7" class="slide level2 smaller">
+<section id="section-3" class="slide level2 smaller">
 <h2></h2>
 <p><strong>ReLU function</strong></p>
 <p><span class="math display">\[
@@ -562,7 +600,7 @@ <h2></h2>
 <li>It is a popular activation function used in deep learning models.</li>
 </ul>
 </section>
-<section id="section-8" class="slide level2 smaller">
+<section id="section-4" class="slide level2 smaller">
 <h2></h2>
 <p><strong>Feedforward Neural Network</strong></p>
 <div class="cell" data-reveal="true" data-fig-width="5" data-fig-height="3" data-layout-align="center">
@@ -639,7 +677,7 @@ <h2>Feedforward Neural Network</h2>
 <li>The weights and biases are learned during the training process.</li>
 </ul>
 </section>
-<section id="section-9" class="slide level2 smaller">
+<section id="section-5" class="slide level2 smaller">
 <h2></h2>
 <p><strong>Loss function</strong></p>
 <ul>